In #2 you state the key is in the ignition. This is the "master" alarm cancel condition. You can't enable the alarm with the key in the ignition. To enable the alarm you must remove the key, then press the lock button on the fob (and possibly close the door -- not sure on that one).The answers to your questions:
1.- There is no padlock symbol appearing when I am the alarm o lock the doors with the FOB.
2.- The map lights turn on when I open the door. And yes.... If the key is in the ignition and I open the door I get a chime.
3.- The trunk release button in the glove box doesn't work. 😕
Thank you for your help.
Also, in one of your previous replies, you mentioned unlocking through the open window, but that isn't really specific enough for debugging. Did you lift the lock knob, or press the driver side unlock switch, or just open the inside door handle? The debug logic might differ between those 3 options, and for those trying to duplicate your problem on their cars, might be relevant.